I speak to cyclists frequently who have been involved in a crash where the police have investigated and reached all the wrong conclusions. You may have been stopped by the police for doing something an officer tells you was improper while riding. Many of these encounters do not go well, typically because the officer is ill-informed of traffic laws affecting cyclists, or is just hostile toward cyclists.
This came up recently in a conversation with a friend who was on a ride with some buddies at 5:30 AM with absolutely no traffic in sight. An officer pulled them over and told them they were required to ride single file. When they pointed out he was ill-informed about cycling laws, the officer threatened to issue them citations. They did the right thing... they rode off single file.
I have been involved in many cases in which the officer made factual mistakes as to what happened or who said what, or where the facts were correct, but the officer misunderstood the law. I am currently handling such a situation for a client.
It is not uncommon for the officer to simply get it wrong, which is particularly frustrating for a cyclist who is more informed on traffic laws than the officer. However, the officer has a badge and the ability to issue a ticket or make an arrest. It does not pay to argue with the officer. These are the types of arguments cyclists don't win and they can often escalate unnecessarily. The police officer always gets the last word on the scene.
An uninformed police officer is not likely to suddenly see the light of reason because a cyclist points out his mistake, particularly if the cyclist does it by getting in the officer's face (an entirely normal reaction when dealing with ignorance). When it is clear the officer is going to pursue a course of action with which you do not agree, you are better to walk away and let him do what he is determined to do.
In situations where a police report is prepared without including the cyclist's statement, you can always submit a written statement to the officer and request it be added to the report. You can also take it up with a supervisor; just don't expect the report to be corrected or re-written.
If you are given a ticket you feel is improper, you clearly should challenge it in court. If the officer is inaccurate in preparing an accident report, you must deal with an experienced cycling crash attorney who will know what steps need to be taken to protect you.